By Lisa Beyer--Reported by Michael Duffy and Dan Goodgame/ Washington and Gavin Scott/Chicago

As the battle grinds on in the gulf, thoughts of a quick solution irresistibly spring to mind. Why not assassinate Saddam? Or threaten to nuke Baghdad? Or carpet bomb the Iraqis to kingdom come? The U.S., in fact, does have potent weapons that have not yet been unsheathed. "We have a toolbox that's full of lots of tools, and I brought them all to the party," General Colin Powell said last week. Field commander H. Norman Schwarzkopf bragged, "We could end the war in two days, but we don't want to destroy Iraq."

The U.S. and its coalition partners are also worried that a lethal knockout punch to Saddam would turn him into an even greater hero on the Arab street than he already is. And though the allies view their campaign in the gulf as just, there are moral limits to the conduct of war, even when confronting an opponent who behaves as despicably as Saddam. "Military professionals have a very strong sense of what distinguishes the work they do from butchering," says Michael Walzer, a professor of social science at the Institute for Advanced Study in Princeton, N.J. "It is a moral sense, even though it's entangled with professional pride and a sense of what works and what doesn't." Still, if the allied strategy of waging a fair fight should fail, the war's prosecutors may come under pressure to resort to more drastic means.

1. Should Saddam Hussein Be Assassinated?

Ordering a hit on any particular person, even one as diabolical as Saddam, is dirty business. But assuming Saddam's death would stop the Iraqi war machine cold, it would mean one life in exchange for the thousands, or tens of thousands, who might die if the battle continued. British Prime Minister John Major spoke for many people around the world when, alluding to the prospect of Saddam's murder, he said, "I for one will not weep for him."

Under a 1981 Executive Order, the U.S. government is forbidden to participate in assassination. But the rules of battle arguably supercede that prohibition. In wartime, international law recognizes military commanders as legitimate targets; as commander in chief of Iraqi forces, Saddam thus qualifies. (Of course, so does President Bush.) Washington's denials notwithstanding, Saddam has been pursued by allied bombers. His presidential palace has been hit; his command-and-control centers have been hit; most of the places allied intelligence thought Saddam might be have been hit.

Saddam reportedly shuttles among half a dozen underground bunkers--including one that is luxuriously appointed and designed to withstand a nuclear blast--or hides out in civilian neighborhoods, which he knows the U.S. will not intentionally attack. Israeli military officials say privately that if they were to retaliate for Iraqi assaults on their territory, they would happily go after Saddam. But even with their renowned ability to ferret out foes, the Israelis cannot get a fix on him. "When it was possible, nobody thought of it," says a high-ranking official in Jerusalem, "and now that everybody is thinking of it, it's almost impossible."

The difficulty of zeroing in on Saddam is one reason the Bush Administration has so assiduously denied that it is gunning for him. Washington does not want to declare killing Saddam as a goal and risk failing to achieve it, repeating last year's humiliation of having Manuel Noriega slip through U.S. hands during the invasion of Panama. "Every day that Saddam survived," says a White House official, "would be seen as a victory for him and a loss for us."

There are other compelling explanations for Washington's denials. An explicit U.S. threat to kill Saddam might encourage terrorist attacks on U.S. targets, including President Bush, and might subject allied POWs to even worse treatment by Iraq. It could conceivably make assassination a more acceptable political tool. Most important, if the allies are seen to have slain Saddam on purpose, they will make him a martyr among many Arabs. Washington's hope, and it is probably an unrealistic one, is that if Saddam dies "incidentally" in a raid, his canonization can be avoided.

Would a successful strike on Saddam end the war? The assumption of most allied military analysts is that with its leadership decapitated, the Iraqi regime would quickly wither. Saddam has built his government on little else but a cultish loyalty to himself, enforced by fear. There is no deputy waiting in the wings. Saddam's survivors, reared in his school of terror, might rip one another apart competing to replace him, leaving the Iraqi war effort adrift without a pilot. If a clear successor regime does emerge, it might well sue for peace, since the confrontation over Kuwait was of Saddam's making, not some realization of deep-rooted Iraqi ambition. Given the decisive blow Saddam's departure would deal Baghdad, it is safe to assume that the allies in future raids, as in past ones, will try to hit him.

2. Should a Nuclear Bomb Be Used Against Iraq?

Suppose an American offensive against Iraq bogged down in a bloody stalemate, and Saddam turned his chemical or bacteriological weapons against American troops with devastating effect. Might the U.S. then use nuclear weapons in retaliation and to shorten the war?

No, say Pentagon planners. Publicly, U.S. officials have refused to rule out going nuclear. "We'd prefer to keep Saddam guessing," says an Administration source. But Washington decided early in the confrontation with Iraq not to supply nuclear weapons to the ground troops in Saudi Arabia. Nearly 400 nuclear warheads are thought to be aboard American ships in the gulf region. Using them, however, would yield no military advantage that would come anywhere near offsetting the horrendous political fallout.

For 45 years the U.S. has tried to convince the rest of the world that its dropping of the bombs that incinerated Hiroshima and Nagasaki was an aberration. What's more, the linchpin in Washington's strategy to limit the spread of atomic weapons is a formal promise never to use them against a non-nuclear-armed state. If the U.S. violates its own policy to nuke Iraq, which by all indications does not yet have the Bomb, other countries might rush to develop atomic arms and possibly to use them. At the same time, revulsion over America's use of the ultimate weapon--once again against a non-Western people--would probably shatter the alliance against Saddam.

And what would America gain? Nothing to speak of. Advanced non-nuclear weapons such as fuel-air bombs and cluster bombs can do virtually as much damage to battlefield targets as nukes would. The only sites a nuclear device could eliminate more effectively are cities, for instance Baghdad or Basra. Today's city-aimed missile would not necessarily pack the wallop of Little Boy, the 12.5-kiloton A-bomb that fell on Hiroshima. But even a 2-kiloton package would kill thousands of civilians, violating the most basic rule of war: non-combatants are not fair game.

Similar arguments apply to a retaliatory use of chemical weapons. Though being ripped apart by shrapnel is a horrible way to die, the prospect of an agonizing death from nerve gas is somehow more frightening. Unlike explosives, chemicals can drift into civilian areas. If the U.S. were to unholster these weapons, it would have a hard time continuing its campaign to ban them altogether after the war. And like nukes, there is nothing chemicals can achieve militarily that cannot be accomplished with more acceptable arms.

3. Should Carpet-Bombing Raids Be Expanded?

If replying to Saddam with weapons of mass destruction is unacceptable, an alternative is the old-fashioned method of leveling great swaths of territory with non-nuclear bombs.

The allies are already carpet bombing the more than 100,000 Iraqi Republican Guards massed at the Kuwait-Iraq border. The hope is that if the Guards are hit hard enough, the whole Iraqi military will crumble. If not, it may become necessary to bomb Iraq's frontline troops as well in preparation for an allied ground assault. Whereas the Republican Guards are fiercely loyal to Saddam and have profited from his patronage, the soldiers holding down Kuwait are mainly conscripts, some of them as young as 17. According to defectors, many are anything but gung-ho to fight. War theorists make no distinction between a cynical professional soldier and an innocent, reluctant one. "Anyone in a uniform is a fair target," says Nicholas Fotion, a professor of military ethics at Emory University. But other analysts see a gray area. Says ethicist Robin Lovin, an associate professor at the University of Chicago Divinity School: "I'm not sure that carpet bombing conscripts is morally different from bombing civilians."

And what about retaliating for an Iraqi chemical or biological strike by going after civilians? There are circumstances that military theorists believe justify a breach of the hands-off rule on noncombatants. This would be a situation in which a country faces not just defeat but the destruction of its people, society or culture as, for instance, Britain did at the hands of the Nazis in the early 1940s. But the allied attacks on German cities such as Dresden toward the end of World War II are now widely considered unwarranted because it was clear by then that the allies would win. Likewise, some military ethicists today believe the nuclear strikes on Nagasaki and Hiroshima were unjust.

For the U.S. and its Western allies, the stakes in the gulf will never approach what they were for Britain in World War II. And given the vast superiority and variety of weapons the allies have to fight Saddam, it is hard to imagine them finding themselves in a state of desperation. "I can't see any realistic way that Saddam could put us in a position where we would want to fight a dirty war," says Fotion. "Let him abuse prisoners, attack cities, use poison gas. We have plenty of ways to fight him and still hold the high moral ground." That is not only the most pious place to be, but it is also the best vantage point from which to begin to reorder the postwar world.